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In this study, we introduce and evaluate a novel extractive text summarization methodology, "SummarEyes," based on the visual interaction of the user with the text, using eye-tracking data, as opposed to the traditional approaches based on analysis of textual content only. We conducted a large-scale user study aiming to collect eye-tracking data while reading the text to be summarized. We utilized various user's implicit attention metrics to generate novel eye-tracking-based text summarization models and compared them both to eye-tracking models typically using only a single feature of the gaze duration and to traditional, as well as state-of-the-art summarization methods, based solely on textual features. The models' quality was evaluated in terms of ROUGE scores using intrinsic evaluation on the datasets we had generated, relating gaze behavior to personalized and DUC gold-standard summaries. The experimental results showed that "SummarEyes" significantly outperformed the other summarizers in predicting both the user's personalized summarization and the generic gold standard summaries. With the increasing availability of eye-tracking technology, this research can lead to a new generation of effective user-centric text summarization tools. [ABSTRACT FROM AUTHOR]